Finite-temperature relativistic nuclear field theory: an application to the dipole response

Nuclear response theory beyond the one-loop approximation is formulated for the case of finite temperature. For this purpose, the time blocking approximation to the time-dependent part of the in-medium nucleon-nucleon interaction amplitude is adopted for the thermal (imaginary-time) Green's function formalism. We found that introducing a soft blocking, instead of a sharp blocking at zero temperature, brings the Bethe-Salpeter equation to a single frequency variable equation also at finite temperatures. The method is implemented self-consistently in the framework of Quantum Hadrodynamics and designed to connect the high-energy scale of heavy mesons and the low-energy domain of nuclear medium polarization effects in a parameter-free way. In this framework, we investigate the temperature dependence of dipole spectra in the even-even nuclei $^{48}$Ca, $^{120}$Sn and $^{132}$Sn with a special focus on the giant dipole resonance's width problem and on the low-energy dipole strength distribution.